TY - GEN

T1 - Composing semi-algebraic O-minimal automata

AU - Casagrande, A.

AU - Corvaja, P.

AU - Piazza, C.

AU - Mishra, B.

PY - 2007

Y1 - 2007

N2 - This paper addresses questions regarding the decidability of hybrid automata that may be constructed hierarchically and in a modular way, as is the case in many exemplar systems, be it natural or engineered. Since an important step in such constructions is a product operation, which constructs a new product hybrid automaton by combining two simpler component hybrid automata, an essential property that would be desired is that the reachability property of the product hybrid automaton be decidable, provided that the component hybrid automata belong to a suitably restricted family of automata. Somewhat surprisingly, the product operation does not assure a closure of decidability for the reachability problem. Nonetheless, this paper establishes the decidability of the reachability condition over automata which are obtained by composing two semi-algebraic o-minimal systems. The class of semi-algebraic o-minimal automata is not even closed under composition, i.e., the product of two automata of this class is not necessarily a semi-algebraic o-minimal automaton. However, we can prove our decidability result combining the decidability of both semi-algebraic formulae over the reals and linear Diophantine equations. All the proofs of the results presented in this paper can be found in [1].

AB - This paper addresses questions regarding the decidability of hybrid automata that may be constructed hierarchically and in a modular way, as is the case in many exemplar systems, be it natural or engineered. Since an important step in such constructions is a product operation, which constructs a new product hybrid automaton by combining two simpler component hybrid automata, an essential property that would be desired is that the reachability property of the product hybrid automaton be decidable, provided that the component hybrid automata belong to a suitably restricted family of automata. Somewhat surprisingly, the product operation does not assure a closure of decidability for the reachability problem. Nonetheless, this paper establishes the decidability of the reachability condition over automata which are obtained by composing two semi-algebraic o-minimal systems. The class of semi-algebraic o-minimal automata is not even closed under composition, i.e., the product of two automata of this class is not necessarily a semi-algebraic o-minimal automaton. However, we can prove our decidability result combining the decidability of both semi-algebraic formulae over the reals and linear Diophantine equations. All the proofs of the results presented in this paper can be found in [1].

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U2 - 10.1007/978-3-540-71493-4_57

DO - 10.1007/978-3-540-71493-4_57

M3 - Conference contribution

AN - SCOPUS:38049162559

SN - 9783540714927

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 668

EP - 671

BT - Hybrid Systems

PB - Springer Verlag

T2 - 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007

Y2 - 3 April 2007 through 5 April 2007

ER -